(3x^2y^3+4x)dx+(3x^3y^2+8y)dy=0

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Solution for (3x^2y^3+4x)dx+(3x^3y^2+8y)dy=0 equation: 


Simplifying
(3x2y3 + 4x) * dx + (3x3y2 + 8y) * dy = 0

Reorder the terms:
(4x + 3x2y3) * dx + (3x3y2 + 8y) * dy = 0

Reorder the terms for easier multiplication:
dx(4x + 3x2y3) + (3x3y2 + 8y) * dy = 0
(4x * dx + 3x2y3 * dx) + (3x3y2 + 8y) * dy = 0
(4dx2 + 3dx3y3) + (3x3y2 + 8y) * dy = 0

Reorder the terms for easier multiplication:
4dx2 + 3dx3y3 + dy(3x3y2 + 8y) = 0
4dx2 + 3dx3y3 + (3x3y2 * dy + 8y * dy) = 0
4dx2 + 3dx3y3 + (3dx3y3 + 8dy2) = 0

Combine like terms: 3dx3y3 + 3dx3y3 = 6dx3y3
4dx2 + 6dx3y3 + 8dy2 = 0

Solving
4dx2 + 6dx3y3 + 8dy2 = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), '2d'.
2d(2x2 + 3x3y3 + 4y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

Move all terms containing d to the left, all other terms to the right.

Simplifying
d = 0

Subproblem 2
Set the factor '(2x2 + 3x3y3 + 4y2)' equal to zero and attempt to solve:

Simplifying
2x2 + 3x3y3 + 4y2 = 0

Solving
2x2 + 3x3y3 + 4y2 = 0

Move all terms containing d to the left, all other terms to the right.

Add '-2x2' to each side of the equation.
2x2 + 3x3y3 + -2x2 + 4y2 = 0 + -2x2

Reorder the terms:
2x2 + -2x2 + 3x3y3 + 4y2 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 3x3y3 + 4y2 = 0 + -2x2
3x3y3 + 4y2 = 0 + -2x2
Remove the zero:
3x3y3 + 4y2 = -2x2

Add '-3x3y3' to each side of the equation.
3x3y3 + -3x3y3 + 4y2 = -2x2 + -3x3y3

Combine like terms: 3x3y3 + -3x3y3 = 0
0 + 4y2 = -2x2 + -3x3y3
4y2 = -2x2 + -3x3y3

Add '-4y2' to each side of the equation.
4y2 + -4y2 = -2x2 + -3x3y3 + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = -2x2 + -3x3y3 + -4y2

Simplifying
0 = -2x2 + -3x3y3 + -4y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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